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A Generalized Flux Function for Three-dimensional Magnetic Reconnection

Yeates, AR; Hornig, G

A Generalized Flux Function for Three-dimensional Magnetic Reconnection Thumbnail


G Hornig


The definition and measurement of magnetic reconnection in three-dimensional magnetic fields with multiple reconnection sites is a challenging problem, particularly in fields lacking null points. We propose a generalization of the familiar two-dimensional concept of a magnetic flux function to the case of a three-dimensional field connecting two planar boundaries. In this initial analysis, we require the normal magnetic field to have the same distribution on both boundaries. Using hyperbolic fixed points of the field line mapping, and their global stable and unstable manifolds, we define a unique flux partition of the magnetic field. This partition is more complicated than the corresponding (well-known) construction in a two-dimensional field, owing to the possibility of heteroclinic points and chaotic magnetic regions. Nevertheless, we show how the partition reconnection rate is readily measured with the generalized flux function. We relate our partition reconnection rate to the common definition of three-dimensional reconnection in terms of integrated parallel electric field. An analytical example demonstrates the theory and shows how the flux partition responds to an isolated reconnection event.


Yeates, A., & Hornig, G. (2011). A Generalized Flux Function for Three-dimensional Magnetic Reconnection. Physics of Plasmas, 18(10), Article 102118.

Journal Article Type Article
Publication Date Oct 1, 2011
Deposit Date Dec 22, 2011
Publicly Available Date Sep 26, 2012
Journal Physics of Plasmas
Print ISSN 1070-664X
Electronic ISSN 1089-7674
Publisher American Institute of Physics
Peer Reviewed Peer Reviewed
Volume 18
Issue 10
Article Number 102118


Published Journal Article (2.9 Mb)

Copyright Statement
© 2011 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Yeates, A.R. and Hornig, G. (2011) 'A generalized flux function for three-dimensional magnetic reconnection.', Physics of plasmas., 18 (10). p. 102118 and may be found at

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